We study geometries that arise from the natural G2() action on the geometry of one-dimensional subspaces, of non-singular two-dimensional subspaces, and of non-singular three-dimensional subspaces of the building geometry of type C3(), where is a perfect field of characteristic 2. One of these geometries is intransitive in such a way that the non-standard geometric covering theory from [R. Gramlich and H. Van Maldeghem. Intransitive geometries. Proc. London Math. Soc. (2) 93 (2006), 666–692.] is not applicable. In this paper we introduce the concept of fused amalgams in order to extend the geometric covering theory so that it applies to that geometry. This yields an interesting new amalgamation result for the group G2().
© de Gruyter 2008